File size: 1,863 Bytes
bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 | /*@ Import Lean
import Algorithms.house_robber.lean.helper_lib
open scoped SimpleC
*/
/*@ Extern Coq
(RobPrefixValue : list Z -> Z -> Z -> Prop)
(RobPrefixOpt : list Z -> Z -> Z -> Prop)
(HouseRobberDPState : list Z -> Z -> Z -> Z -> Prop)
(HouseRobberAnswer : list Z -> Z -> Prop)
*/
int rob(int *nums, int n)
/*@ With (l : list Z)
Require
0 <= n && n <= 100000 &&
Zlength(l) == n &&
IntArray::full(nums, n, l) &&
(forall (k : Z), (0 <= k && k < n) => (0 <= l[k] && l[k] <= 10000))
Ensure
HouseRobberAnswer(l, __return) &&
0 <= __return && __return <= 1000000000 &&
IntArray::full(nums, n, l)
*/
{
int prev2 = 0;
int prev1 = 0;
/*@ Inv Assert
nums == nums@pre && n == n@pre &&
0 <= n@pre && n@pre <= 100000 &&
Zlength(l) == n@pre &&
IntArray::full(nums, n@pre, l) &&
(forall (k : Z), (0 <= k && k < n@pre) => (0 <= l[k] && l[k] <= 10000)) &&
0 <= i && i <= n@pre &&
0 <= prev2 && prev2 <= 1000000000 &&
0 <= prev1 && prev1 <= 1000000000 &&
HouseRobberDPState(l, i, prev2, prev1)
*/
for (int i = 0; i < n; ++i) {
int take = prev2 + nums[i];
int skip = prev1;
int cur;
if (take > skip) {
cur = take;
} else {
cur = skip;
}
/*@ Assert
nums == nums@pre && n == n@pre &&
0 <= n@pre && n@pre <= 100000 &&
Zlength(l) == n@pre &&
IntArray::full(nums, n@pre, l) &&
(forall (k : Z), (0 <= k && k < n@pre) => (0 <= l[k] && l[k] <= 10000)) &&
0 <= i && i < n@pre &&
take == prev2 + l[i] &&
skip == prev1 &&
0 <= prev2 && prev2 <= 1000000000 &&
0 <= prev1 && prev1 <= 1000000000 &&
0 <= cur && cur <= 1000000000 &&
HouseRobberDPState(l, i + 1, prev1, cur)
*/
prev2 = prev1;
prev1 = cur;
}
return prev1;
}
|